THE ELECTRIC AND LUMINIFEROUS MEDIUM, 
793 
Let us now consider the efiPect of a compressional term in the ]iotential energy of 
the medium, of the form 
i ^ f (2 + % + 2) “'"y i ^ f”' 
where — is the compression in the medium. The variation of this term will be 
A I" CT (/ S-r; + Sj/ + n Sz) dS — A [ S.r + — Sj/ + Sz j dr. 
Thus there will be added to tlie right-hand side of the ecpiations of vibration new 
terms, giving in all 
. ddh cm/ , dm 
Pdd + ! - -W - A = 0 
' dt^ dv 
_L 
P + 
dy dz 
drdf ddh 
dx 
dm 
did ' dz dx ^dy~^ 
d-^ dhd/ __ dcdf 
^ df~ dx ~ dy 
.dm 
A -T = 0. 
dz 
It follows that Ts satisfies the ecpiation 
d~m . , 
p —- — AV OT ; 
so that the compre.5sional wave is propagated independently of the rotation.al one, of 
which the circumstances are given by equations of the type 
P~f 
P df~ ~ 
dL I 
dx \ dx 
In the discussion of the reflexion of light it has been shown that the same absolute 
separation of compression and rotation is manifested in the passage across an inter¬ 
face into a new medium ; so that however heterogeneous the medium be rendered by 
the presence of vortex-atoms, these two types of disturbance are still quite independent 
of each other. 
The alteration in the electrostatic equations which would be produced by this 
compressional'quality has already been given; if the value of the modulus A is 
extremely great, this alteration will .be quite unnoticeable. In that case, waves of 
compression will be propagated with extremely great velocity, so that as regards 
compression the medium will assume almost instantly an equilibrium condition, for 
which therefore = 0. 
It follows that the value of the integral Idzo/dii . c/S is the same for all boundaries 
MDCCCXGIV.—A. 5 I 
